A meeting of the BP board is due on July 26, when it will discuss Hayward's resignation.
Tony Hayward, 53, became BP's chief executive in 2007. He was strongly criticized for being responsible for the world's most terrible environmental tragedy and deaths of 11 men working on the BP rig, which exploded in the Gulf of Mexico.
A blast ripped through the Deepwater Horizon oil drilling platform, owned by British Petroleum (BP), in late April, causing an oil spill in the Gulf of Mexico, the worst in the history.
BP acknowledged its responsibility for the clean-up, whatever the costs.
The company has received almost 116,000 claims from residents of the Gulf Coast and made over 67,500 payments, totaling $207 million.
To date, BP said the clean-up operations have recovered a total of approximately 807,143 barrels (33.9 million gallons) of oil.
On June 16, BP announced an agreed package of measures, including the creation of a $20 billion escrow account to satisfy certain obligations arising from the oil and gas spill.
Officials in charge of the clean-up said the oil continues to leak from the seabed near the stricken BP well, which was capped last week.